Use synthetic division to find all the real zeros of the polynomial.
f(x) = x³ + x² - 8x - 6
Answers
so hmmm we look at hmm x³ + x² - 8x - 6 so how do squeak out a factor out of it, well, using the rational root test and using our p/q checking for factors, we find that likely factors can be ± 6/1 and ±(3, 2, 1) / 1, anyhow so we check some of those and hopefully without boring you to death we find that -3 works, we can always use the remainder theorem to check if that's true, by simply plugin in f(-3) and if it's indeed a factor, that'd give us 0, well, f(-3) = -27 + 9 +24 +6 = 0, holly smokes!! is a factor.
well, all that jazz means that -3 is a factor, namely the factor is really x = -3 or x + 3 = 0 so the factor is (x+3) and for our synthetic division we'll use the -3 version, Check the picture below.
so we end up with the factors of (x+3)(x²-2x-2), now for the 2nd factor what we can do to break it up is use the quadratic formula
[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-2}x\stackrel{\stackrel{c}{\downarrow }}{-2} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}[/tex]
[tex]x= \cfrac{ - (-2) \pm \sqrt { (-2)^2 -4(1)(-2)}}{2(1)} \implies x = \cfrac{ 2 \pm \sqrt { 4 +8}}{ 2 } \\\\\\ x= \cfrac{ 2 \pm \sqrt { 12 }}{ 2 }\implies x=\cfrac{2\pm\sqrt{2^2\cdot 3}}{2}\implies x=\cfrac{2\pm 2\sqrt{3}}{2}\implies x=1\pm\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} (x+3)(x-1+\sqrt{3})(x-1-\sqrt{3}) \end{array}}~\hfill[/tex]
now, just to clarify, all those are real roots, and the last two come from simply setting x = 1 ± √3 to 0 to get the factors.
Related Questions
The scale on a map of Florida is 2 inches = 50 miles. What is the distance in miles
represented by a length on the map of 7 inches?
Answers
The distance in miles represented by a length on the map of 7 inches is 0.28
What is scale factor?The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.
Given;
The scale of a map says that 2 inches represents 50 miles.
2 inches = 50 miles
1 Mile = 2/50 inches
Hence, 7 Mile = 7 * 2/50 inches
7 Mile = 14/50 inches
7 Mile = 0.28 inches
Therefore, the scale factor of 7miles in the map will be 0.28inches
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How is the graph of y=3x^2+3 different from the graph of y=3x^2
Answers
Answer:
Step-by-step explanation:
y=3x^2 has a parabolic graph with its vertex at the origin, (0, 0).
y=3x^2 + 3 has the same graph shape, but its vertex and every other point are 3 units higher (away from the origin) up.
You buy clothing at a sale. You buy sneakers at 2 3 of their original price of $60, a sweater at 7 10 of its original price of $35, and a jacket at 5 6 of its original price of $45. Answer each question and show all your work. How much money did you spend
Answers
We spent a total of 40.2 + 24.5+ 37.8 = $102.50
Explain about the fractions?A fraction is a metric unit for describing a piece or component of a whole. It represents the appropriate parts of the totality. A fraction is made up of two parts: the numerator and the denominator. The number at the top is the numerator, and the number at the bottom is the denominator.
Fractions are used to represent the parts of an entity or collection of entities. The components of a fraction are two. The figure at the top of the line is the numerator. It provides information on how many equal sections from the total or collection were taken. The number that appears below the line is the denominator.
We multiply the initial price by the fractions' decimal conversions to determine how much we spent. The quantities are then combined.
You purchased sneakers for $60 and paid 2/3 of that amount, or $0.6666, for a total of $40.20, saving $19.80.
Sweater costs $35 and you paid $7.50 for it, saving you $10.50. 35(0.7)=$24.50.
You paid $45 for a jacket, and since 5/6=0.8333, 45(0.84)=$37.80, you made a $7.20 profit.
We spent a total of 40.2 + 24.5+ 37.8 = $102.50
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Is algebra.
PLEASE HELP NO LINKS OR FILES.
I don't want links.
I don't want links.
I don't want links.
I don't want links.
Answers
Question 4 is B
Answer:
for question 3 - b
for question 4- b
Step-by-step explanation:
4 Select the correct answer. Annabelle wanted to find out how many people in her neighborhood were going to the rock concert over the weekend. She asked a couple of her immediate neighbors. On the basis of the answers she got, she drew her conclusion. What kind of statistical investigation did Annabelle perform
Answers
Annabelle collected data from a sample of people that were convenient for her to access, such as her immediate neighbors, and used this to draw her conclusion.
Annabelle performed a convenience sample investigation, which is a type of statistical investigation. This involves collecting data from a sample of people that are convenient for the researcher to access. In this case, Annabelle asked a couple of her immediate neighbors to find out how many people in her neighborhood were going to the rock concert..
Convenience sampling is useful when time or resources are limited, however the results may not be representative of the larger population. Therefore, it is important to consider the limitations of the sample when drawing conclusions. For example, Annabelle may not have considered that the neighbors she asked may not be representative of the whole neighborhood.
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Determine the slope, x-intercept and y-intercept of the line given by the equation 2x+3y=6
Answers
Y-intercept = 2
Slope = -2/3x
X-intercept = 3
To make it easier, write the equation in slope-intercept form (y = Mx + b)
1. Subtract 2x on both sides
3y = 6 - 2x
2. Divide both sides by 3 to get y by itself
3y/3 = 6 - 2x/3
3. Simplify
y = 2 - 2/3x
4. Reorder numbers on the right into slope-intercept form
y = -2/3x + 2
5. Using the information, m = slope and b = y-intercept, find the slope and y-intercept.
Since -2/3 = m, the slope is -2/3 and 2 = b, the y-intercept is 2.
5. To find the x-intercept, set y = 0
0 = -2/3x + 2
6. Subtract two on both sides
-2 = -2/3x
7. Multiply both sides by 3 to get rid of the fraction
-6 = -2x
8. Divide by -2 on both sides to find x
X = 3
Can some kind person help me on this assignment pls
Answers
Answer:
D, B
Step-by-step explanation:
Question 8.
The shaded area should be on or below the line [tex]y=\frac{5}{2}x-2[/tex] AND below but not on the line [tex]y=\frac{1}{2}x+2[/tex]
Question 9.
See the attached image.
Shade on or under the line [tex]y=\frac{1}{2}x-1[/tex] AND above but not on the line [tex]y=\frac{3}{2}x+1[/tex].
plz help lol i’m stuck
Answers
Answer:
the length of arc=
[tex]2\pi \times 6 \times \frac{60}{360} \\ 2\pi[/tex]km
The surveyor walked 120 ft away from one of the sensors so that her walking path made a 90 degree angle with the width of the lake when she stop she measured the lake when she stopped she measured the angle between her lines of sight to both sensors and it was 70 degrees
Answers
Therefore ,the answer to the above trigonometry issue is therefore that the river is 70 feet wide.
What is trigonometry?The study of the connections between the angles and sides of triangles is known as trigonometry. Due to the fact that each straight-sided figure may be reduced to a collection of triangles, trigonometry is commonly utilized in geometry. There are a mind-boggling number of connections between trigonometry and other branches of mathematics, especially algebra, real or complex, integrals, logarithms, and infinite series.
Here,
Figure depicts a right triangle which, in relation to angle, its next side has length d or its wrong side is equal to the river's width, y. As a result,
tanθ= d/ y
=> y=dtanθ
=> y = (100m)tan(35.00)=70ft
The river measures 70 feet in width.
As a result, the trigonometry problem's answer indicates that the river's width is 70 feet.
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Given the following system of equations, solve for 'X', 'y' and 'z.
2x - 32= -18
-4y + 2z = 4
3x + 10y= 1
Answers
x=7, y=-2, and z=-2
just trust me on it
-4y+2z=4 2z=4-4y z=2-2y
3x+10y=1 3x= 1-10y x= 1/3-10/3y
HELP ME PLS ILL GIVE YOU BRAINLIST
Answers
An object has a mass of 440 kg and a volume of 11 m3.
Find the density of the object in kg/m3.
Answers
Answer:
40 kg/m³
Step-by-step explanation:
To find the density divide the mass by the volume
440kg / 11 m³ = 40 kg/m³
Answer:
40 Kg/m cube
Step-by-step explanation:
Beth and Amy's tennis coach is picking 2 athletes from the 10 on the tennis team to speak at an assembly. What is the probability the coach will pick Beth and Amy?
Answers
Answer:
Is it beth AND amy or Beth OR Amy?
On a number line, suppose point E has a coordinate of -3 and EG=4. What are the possible coordinates of point G?
Answers
Answer:
[tex]-1\frac{1}{3}[/tex]
Step-by-step explanation:
We can approach this equation algebraically. Since we know E = -3, we can substitute it into our Second equation, giving us:
-3G = 4
Divide both sides by 3 gives us :
G = [tex]-\frac{4}{3}[/tex] = [tex]-1\frac{1}{3}[/tex]
So, the possible coordinate of G is [tex]-1\frac{1}{3}[/tex].
Hope this helped!
Pls help pls help pls I’m begging
Answers
and that B) is 27.8
Answer:
side=8 unit
Area=777 unit^2
SEE IMAGE FOR SOLUTION
Hope it helps
Have a great day
Mrs. Hanover borrows $1,413 at a
rate of 5% per year. How much
Simple Interest will she owe if it
takes her 9 months to repay the
loan? Round your answer to the
nearest cent
Answers
well, let's recall that a year has 12 months, so 9 months is really 9/12 of a year
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1413\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\to \frac{9}{12}\dotfill &\frac{3}{4} \end{cases} \\\\\\ I = (1413)(0.05)(\frac{3}{4}) \implies I = 1413(\frac{3}{80})\implies I\approx 52.99[/tex]
Ellis put 57 equal size bags of potatoes onto the shelf at the grocery store. The total weight was 60.42 pounds. What is the weight of each bag of potatoes
Answers
Answer: 1.06 pounds per bag of potatoes
Step-by-step explanation:
Total weight = 60.42
# of bags of potatoes = 57
60.42/57 = 1.06 pounds per bag
2) What is the additive inverse of 4,000,000 ?
a) 4,000,000
b) -4,000,000
Answers
Answer:
B
Step-by-step explanation:
Answer:
(b) -4,000,000
Step-by-step explanation:
Additive inverse is what you add to a number to make the sum zero. In other words, we just need to change the sign of the number to find its additive inverse, from - to + and from + to -
PLEASEEE ANSWERRR ASAP
If point A(-3, 9) is dilated by a scale factor of 6 with the origin as the center of
dilation, what would be the coordinates of the new image at point A'?
Answers
Answer:
A' = (-18, 54)
Step-by-step explanation:
If 1 and -2 are zeroes of x^2+ax+b=0. Find a and b. First and correct answer will be marked brainliest.
Answers
Answer:
a = 1, b = -2
Step-by-step explanation:
You are given values of x are 1 and 2 when the equation is 0
To solve the problem substitute the values of x into the equation
For x =1
1^2 + a(1) + b = 0
1 + a + b = 0
a+b = -1(call this equation i)
For x = -2
-2^2 + a(-2) + b = 0
4 - 2a + b = 0
-2a + b = -4 (call this equation ii)
Now solve equation i and ii simultaneously to get values of a and b.
a+b = -1
-2a+b = -4
By elimination method (also you can solve by substitution method) subtract equation ii from equation i, we get
3a = 3
Divide 3 both sides, you get
a = 1
Take the value of a above substitute it into either equation i or ii to get the value of b
Here i considered equation i
a + b = -1
1 + b = - 1
b = - 1 - 1
b = -2
Therefore a = 1, b = -2
What is the value of S3= infinity sigma n-1 5(1/3)^n-1
Answers
Write the equation of the line that passes through the points (6, 1) and
(6, -8). Put your answer in fully simplified point-slope form, unless it
is a vertical or horizontal line.
Answers
something noteworthy is that the x-coordinate is the same for each point, so Check the picture below.
The population for Rainbow City is 36,000. The growth rate is 3%. About how many people will it have after 5 years
Answers
Answer:
41,500 people
Step-by-step explanation:
First you find 3% of 36,000= 1,080
Then you do 1080 x 5= 4,500
Then finally do 36,000 + 4,500= 41,500
Use the distributive property to fill in the blanks below. Pls help me :| This is for a grade and today for me is the last day of school :|
Answers
Answer:8 in each box
Step-by-step explanation:
U are multiplying 2 and 7 each by 8
The formula for the area of a triangle is A=12bh. Which equation shows the formula solved for h?
Answers
Answer:
h=1/2Ab
Step-by-step explanation:
Why 1 [infinity] is not defined?
Answers
1 [infinity] is not defined because infinity is an abstract concept and cannot be used in the same way as numeric values. Infinity is not a number or a numerical value, and therefore it cannot be used in equations or arithmetic operations.
1. Infinity is an abstract concept and cannot be used in the same way as numeric values.
2. Infinity is not a number or a numerical value.
3. Therefore, it cannot be used in equations or arithmetic operations.
4. Therefore, 1 [infinity] is not defined.
1 [infinity] is not defined because infinity is an abstract concept and cannot be used in the same way as numeric values. Infinity is not a number or a numerical value, and therefore it cannot be used in equations or arithmetic operations.
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... due tomorrow... help pls
Answers
Where is quadrant 4?
Answers
The fourth quadrant, often known as Quadrant IV, is the bottom right quadrant. The x-axis in this quadrant is positive, whereas the y-axis is negative.
Two-dimensional Cartesian axes separate the plane into four infinite areas known as quadrants, each of which is bordered by two half-axes. These are frequently numbered 1 through 4.
90° arc; one-fourth of a circle. the region enclosed by such an arc and two sketched radii, one at each extreme. a component of a machine that has a quarter-circle form.
The x- and y-coordinates are both positive in quadrant I.
The x-coordinate is negative and the y-coordinate is positive in quadrant II.
The x- and y-coordinates are positive in quadrant III.
Quadrant IV: The x-coordinate is positive and the y-coordinate is negative.
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I keep getting this question wrong. Anyone can help me answer what the answer is?
Answers
Study the example showing a function. Then solve
problems 1-6.
Example
The table and graph show the
relationship between the length
of the sides of a square, in feet, and
the perimeter of the square in feet.
Side Length (input) 1 2 3 4 S
Perimeter (output) 4
812 16 20
The relationship is a function because
there is only one output value for
each input value.
Perimeter (output)
20
18
16
14
12
10
8
6
4
2
Perimeters of Squares
0 1 2 3 4 5 6 7 8 9
Side Length (input)
1 Describe the relationship between the input and output
values in the example.
2 Can you represent the function in the example with an
equation? If so, what equation can you write? If not,
why not?
Vocabulary
function a rule that
Answers
The relationship between the input and output is that the perimeter of a square is always equal to four times the length of one of its sides.
What is the perimeter of square?The perimeter of a square is the total distance around the outside of the square. It is the sum of the lengths of all four sides. To find the perimeter of a square, you simply multiply the length of one side by four, since all sides of a square are equal in length. The formula is P=4S
1.The relationship established between (side length of the square) and output (perimeter of the square) represent that A square's perimeter is always equal to 4 times one of its sides.
2.Yes, the function can be represented with an equation. The equation would be:
Perimeter = 4 × Side Length.
Side Length (input) 1 2 3 4 5
Perimeter (output) 4 8 12 16 20
This equation states that the perimeter of a square is equal to four times the length of one of its sides.
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